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Question

Two circles x2+y2+2g1x+2f1y+c1=0 and x2+y2+2g2x+2f2y+c2=0 are said to be orthogonal. Then 2g1g2+2f1f2=c1+c2


A

True

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B

False

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Solution

The correct option is A

True


Given circles x2+y2+2g1x+2f1y+c=0 .......(1)

x2+y2+2g2x+2f2y+c=0 ............(2)

Let C1& C2 be the centers and r1& r2 radii of circle (1) and (2) respectively. P& Q is the point of

intersection of two circles

C1(g1f1)

C2(g2f2)

r1=g21+f21c1,r2=g22+f22c2

C1P=r1

C2P=r2

Right angle triangle C1PC2

(c1c2)2=r21+r22

(g1g2)2+(f1f2)2=g21+f21c1+g22+f22c2

2g1g2+2f1f2=c1+c2

So, give statemebt is correct.


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